Correction method for image forming apparatus

ABSTRACT

A correction method for an image forming apparatus including: a light source including light emitting points, a photosensitive member configured to rotate in a first direction, and a deflecting unit configured to deflect light beam emitted from the light source in a second direction orthogonal to the first direction to form scanning lines, the correction method including a correction step of correcting sparseness and denseness of density in the first direction caused by deviation of the scanning lines by moving a predetermined pixel in the first direction in accordance with the deviation, and causing a pixel value of the predetermined pixel to be output in accordance with movement of the predetermined pixel, wherein the correction step corrects the sparseness and denseness of the density based on the deviation of the scanning lines and the pixel value of the pixel, which are adjusted in accordance with an image forming condition.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to a correction method for an imageforming apparatus, for correcting distortion and uneven image density ofan image during image formation of a two-dimensional image by the imageforming apparatus, e.g., a digital copying machine, a multifunctionalperipheral, or a laser printer.

Description of the Related Art

In electrophotographic image forming apparatus such as a laser printerand a copying machine, there has been generally known a configuration toform a latent image on a photosensitive member with use of a lightscanning device configured to perform scanning with a laser beam. In thelight scanning device of a laser scanning type, a laser beam collimatedwith use of a collimator lens is deflected by a rotary polygon mirror,and the deflected laser beam is formed into an image on a photosensitivemember with use of an elongated fθ lens. Further, there is knownmultibeam scanning in which a laser light source having a plurality oflight emitting points is included in one package so as to performscanning with a plurality of laser beams simultaneously.

Meanwhile, in order to form a satisfactory image without uneven imagedensity and banding (stripe pattern caused by the difference in imagedensity), it is desired that distances between scanning lines of whichpositions to be scanned with a laser beam are adjacent to each other ina rotational direction of the photosensitive member be equal to eachother. However, the distances between the scanning lines are varied dueto a plurality of factors described below. The distances between thescanning lines on the photosensitive member are varied by, for example,a fluctuation in a surface speed of the photosensitive member, or arotation speed fluctuation of a rotary polygon mirror. Further, thedistances between the scanning lines are also varied by a variation inangle of mirror faces of the rotary polygon mirror with respect to arotary shaft of the rotary polygon mirror and a variation in intervalsbetween light emitting points arranged on a laser light source. To copewith uneven image density and banding caused by such factors, there hasbeen proposed a technology of correcting banding by controlling anexposure amount of the light scanning device. For example, in JapanesePatent Application Laid-Open No. 2012-98622, there is described aconfiguration in which a beam position detection unit configured todetect a beam position in a sub-scanning direction is arranged in thevicinity of the photosensitive member, and the exposure amount of thelight scanning device is adjusted based on scanning distance informationobtained from a detected beam position, to thereby make banding lessnoticeable.

Similarly to Japanese Patent Application Laid-Open No. 2012-98622described above, as a configuration to make banding less noticeable bycontrolling an exposure amount, there is given a configuration tocorrect the positions of scanning lines by shifting image data in thesub-scanning direction in accordance with position information in thesub-scanning direction of each scanning line. In an electrophotographicimage forming apparatus, banding is caused also by image positionaldeviation of from about 2 μm to about 5 μm. For example, in an imageforming apparatus having a resolution of 1,200 dpi, the width of onepixel is 21.16 μm, and hence in order to correct the image positionaldeviation of from about 2 μm to about 5 μm, it is necessary to move animage gravity center with a resolution of 1/10 pixel or less. Meanwhile,when the image gravity center is moved by shifting (adding) image data,the movement amount of the image gravity center with respect to theimage data to be added may be varied depending on the photosensitivemember and the developing process conditions.

In FIG. 15A, exposure distributions (exposure areas) of two adjacentscanning lines overlap each other to form a composite light spot B inwhich light spots in the two scanning lines are added to each other. InFIG. 15B, the exposure amount of the first scanning line is decreased,and a pixel in the third scanning line is newly exposed to light in asmall exposure amount. With this, a composite light spot A, in whichlight spots in the three scanning lines are combined, is formed, and itis understood that, as compared to the composite light spot B of FIG.15A, the image gravity center of the composite light spot A is moved inthe rightward direction of FIG. 15B. FIG. 15C and FIG. 15D are each agraph for showing a comparison of exposure widths and exposure positionsobtained by slicing the composite light spots A and B with developingthreshold values Th1 and Th2. As shown in FIG. 15C, when the compositelight spots A and B are sliced with the developing threshold value Th1,the exposure positions of the composite light spots A and B are slightlyshifted from each other, but the exposure widths thereof aresubstantially the same. Meanwhile, as shown in FIG. 15D, when thecomposite light spots A and B are sliced with the developing thresholdvalue Th2, the exposure width of the composite light spot A becomesslightly thicker (wider) as compared to that of the composite light spotB, and the movement amount of the exposure position in the rightwarddirection of the composite light spot A also becomes larger. Further, asis understood from FIG. 16B, when a developing threshold value changessignificantly at a time when banding correction is performed, the imagedensity decreases in an image area A in which the image gravity centeris moved as compared to that of an image area B in which the imagegravity center is not moved, and a density change occurs. The details ofFIG. 15A to FIG. 15D, and FIG. 16A to FIG. 16C will be described later.

As described above, in the case of performing processing of shiftingimage data by adding image data, there is a problem in that the movementamount also changes due to a change in developing threshold value, andhence banding correction cannot be performed satisfactorily. Such changein developing threshold value is liable to occur due to a change inimage forming conditions, such as a charging amount for charging aphotosensitive member, a developing voltage applied between aphotosensitive member and a developing device, and an exposure lightintensity.

SUMMARY OF THE INVENTION

The present invention has been made under the above-mentionedcircumstances, and it is an object of the present invention to obtainsatisfactory image quality by correcting uneven image density of animage, which occurs in a direction corresponding to a rotationaldirection of a photosensitive member, in accordance with image formingconditions.

According to one embodiment of the present invention, there is provideda correction method for an image forming apparatus,

the image forming apparatus comprising:

-   -   a light source comprising a plurality of light emitting points;    -   a photosensitive member configured to rotate in a first        direction so that a latent image is formed on the photosensitive        member with a light beam emitted from the light source; and    -   a deflecting unit configured to deflect the light beam emitted        from the light source to move light spots of the light beam        radiated to the photosensitive member in a second direction        orthogonal to the first direction to form scanning lines,

the correction method comprising a correction step of correctingsparseness and denseness of density in the first direction caused bydeviation of the scanning lines in the first direction by moving apredetermined pixel in the first direction in accordance with thedeviation of the scanning lines, and causing a pixel value of thepredetermined pixel to be output in accordance with a movement of thepredetermined pixel,

wherein the correction step comprises correcting the sparseness anddenseness of the density based on the deviation of the scanning linesand the pixel value of the pixel, which are adjusted in accordance withan image forming condition.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a view for illustrating an entire image forming apparatusaccording to first and second embodiments.

FIG. 1B is a view for illustrating a configuration of the periphery of aphotosensitive drum and a light scanning device.

FIG. 2 is a block diagram of the image forming apparatus according tothe first and second embodiments.

FIG. 3 is a diagram for illustrating positional deviation of scanninglines according to the first and second embodiments.

FIG. 4 is a block diagram for illustrating a step of storing informationin a memory according to the first and second embodiments.

FIG. 5 is a time chart for illustrating one scanning period according tothe first and second embodiments.

FIG. 6 is a flowchart for illustrating processing of calculating apositional deviation amount according to the first and secondembodiments.

FIG. 7 is a flowchart for illustrating correction processing accordingto the first and second embodiments.

FIG. 8A, FIG. 8B, FIG. 8C, and FIG. 8D are each a diagram forillustrating positional deviation of pixels for each classificationaccording to the first and second embodiments.

FIG. 9A and FIG. 9B are each a graph for showing coordinatetransformation of pixel positions in a sub-scanning direction accordingto the first and second embodiments.

FIG. 10A, FIG. 10B, FIG. 10C, and FIG. 10D are each a graph for showingcoordinate transformation of pixel positions in the sub-scanningdirection according to the first and second embodiments.

FIG. 11A and FIG. 11B are each a graph for showing coordinatetransformation of pixel positions in the sub-scanning directionaccording to the first and second embodiments.

FIG. 12A, FIG. 12B, and FIG. 12C are each a graph for showing aconvolution function to be used in filtering according to the first andsecond embodiments.

FIG. 12D is a graph for showing a correction value and a coefficient.

FIG. 13A, FIG. 13B, FIG. 13C, and FIG. 13D are each a diagram forillustrating the filtering for each classification of positionaldeviation according to the first and second embodiments.

FIG. 14A is a view for illustrating a patch density detectionconfiguration according to the first and second embodiments.

FIG. 14B is a graph for showing patch density detection resultsaccording to the second embodiment.

FIG. 15A, FIG. 15B, FIG. 15C, and FIG. 15D are each a graph for showingthe movement of an image gravity center in the conventional art.

FIG. 16A, FIG. 16B, and FIG. 16C are each a table for showing unevenimage density caused by the movement of the image gravity center in theconventional art.

FIG. 17 is a diagram for showing a conversion table for converting imagedata (density data) into drive data for generating a PWM signal.

DESCRIPTION OF THE EMBODIMENTS

First, prior to embodiments described later, problems in theconventional banding correction will be described in detail withreference to FIG. 15A to FIG. 15D and FIG. 16A to FIG. 16C. As describedabove, as a configuration to make banding less noticeable by controllingan exposure amount, there is a configuration to correct the positions ofscanning lines by shifting image data in a sub-scanning direction inaccordance with position information in the sub-scanning direction ofeach scanning line. In an electrophotographic image forming apparatus,banding is caused also by image positional deviation of from about 2 μmto about 5 μm. For example, in an image forming apparatus having aresolution of 1,200 dpi, the width of one pixel is 21.16 μm, and hencein order to correct the image positional deviation of from about 2 μm toabout 5 μm, it is necessary to move an image gravity center with aresolution of 1/10 pixel or less. Meanwhile, when the image gravitycenter is moved by adding image data as described above in theelectrophotographic image forming apparatus, the movement amount of theimage gravity center with respect to the image data to be added may bevaried depending on the photosensitive member and the developing processconditions.

FIG. 15A is a graph for showing an exposure distribution cross-sectionin the sub-scanning direction in a state in which a light beam is lit atpixels in two adjacent scanning lines (hereinafter simply referred to as“pixels are turned on”). The vertical axis of FIG. 15A represents alight intensity, and the horizontal axis represents a position in thesub-scanning direction, which also similarly applies to FIG. 15B. InFIG. 15A, there is shown an exposure distribution formed by a lightscanning device in which a light spot of a light beam has a diameter of70 μm (light spot size) with a resolution of 1,200 dpi. In the case of aresolution of 1,200 dpi, the size (width) of one pixel is 21.16 μm, andhence the light spot size of 70 μm is larger than an interval of pixels.Therefore, when the two scanning lines are turned on, exposuredistributions (exposure areas) of the respective scanning lines overlapeach other to form a composite light spot B in which light spots in thetwo scanning lines are added to each other. In FIG. 15B, as compared tothe composite light spot B shown in FIG. 15A, there is shown an examplein which the exposure amount of the first scanning line is decreased,and a pixel in the third scanning line is newly exposed to light in asmall exposure amount. In FIG. 15B, the third scanning line is exposedto light in a small exposure amount, to thereby form a composite lightspot A in which light spots in the three scanning lines are combined. Itis understood that the image gravity center of the composite light spotA is moved in the rightward direction of FIG. 15B as compared to thecomposite light spot B of FIG. 15A. As described above, through additionof the scanning lines exposed to light in a small exposure amount, theimage gravity center of an image spot to be formed can be moved.

Further, FIG. 15C and FIG. 15D are each a graph for showing a comparisonof the composite light spots A and B. Each vertical axis represents alight intensity, and each horizontal axis represents a position in thesub-scanning direction. Th1 of FIG. 15C and Th2 of FIG. 15D eachschematically represents a threshold value, at which development isperformed through adhesion of a toner, with respect to an exposuredistribution, and the threshold value is hereinafter referred to as adeveloping threshold value. Further, the developing threshold values Th1and Th2 have a magnitude relationship of Th1>Th2. In the composite lightspots A and B shown in FIG. 15C and FIG. 15D, a portion exposed to lightat a light intensity of the developing threshold values Th1 and Th2 ormore are developed with a toner, and a portion exposed to light at alight intensity of less than the developing threshold values Th1 and Th2is not developed with a toner. In FIG. 15C and FIG. 15D, the exposureposition of the composite light spot A indicated by the thick solid lineis moved in the rightward direction of FIG. 15C and FIG. 15D relative tothe composite light spot B indicated by the thin solid line. Further,the exposure distribution of the composite light spot A slightly changesas compared to that of the composite light spot B, and hence the peakexposure amount of the composite light spot A is slightly decreased ascompared to that of the composite light spot B. In comparison ofexposure widths and exposure positions obtained by slicing the compositelight spots A and B with the developing threshold values Th1 and Th2,when the composite light spots A and B are sliced with the developingthreshold value Th1 (FIG. 15C), the exposure positions of the compositelight spots A and B are slightly shifted from each other, but theexposure widths thereof are substantially the same. Meanwhile, when thecomposite light spots A and B are sliced with the developing thresholdvalue Th2 (FIG. 15D), the exposure width of the composite light spot Abecomes slightly thicker (wider) as compared to that of the compositelight spot B, and the movement amount of the exposure position in therightward direction of the composite light spot A also becomes larger.As described above, in the case of performing processing of shiftingimage data by adding image data, there is a problem in that the movementamount also changes due to a change in developing threshold value, andhence banding correction cannot be performed satisfactorily. Such changein developing threshold value is liable to occur due to a change inimage forming conditions, such as a charging amount for charging aphotosensitive drum, a developing voltage applied between aphotosensitive drum and a developing device, and an exposure lightintensity.

Next, an example in which an image shift is performed will be described.FIG. 16A and FIG. 16B are each a table for showing image data to beprinted on a recording material. In each table, the vertical directionrepresents a printing line in a length direction (sub-scanningdirection) of a recording material, and the horizontal directionrepresents pixels in a width direction (main scanning direction) in eachprinting line of the recording material. The numerical values in thetable represent image data of each pixel (density value displayed in 16levels of from 0 to 15). In FIG. 16A and FIG. 16B, there is shown anexample in which an image gravity center is moved downward in the lengthdirection by reducing, relative to the image data of FIG. 16A, the imagedata (density value) in the second and sixth lines by 2 and adding thereduced image data (density value) to the fourth and eighth lines by 2as shown in the table of FIG. 16B. With this, the image gravity centeris moved toward the third line by ⅛ pixel (= 2/16). In theconfiguration, the movement amount of the image gravity center can beadjusted by a data value of image data to be added. That is, when thedata value of the image data to be added is small, a pixel to be exposedin a small exposure amount is added, and the image gravity center ismoved by a small amount. Meanwhile, when the data value of the imagedata to be added is large, a pixel to be exposed to light in a largeexposure amount is added, and the image gravity center is moved by alarge amount. In FIG. 16C, there is shown a state in which density ischanged due to a large change in developing threshold value when bandingcorrection is performed with the above-mentioned image data shown inFIG. 16A and FIG. 16B. In the image area A, the image gravity center ismoved downward in the length direction through banding correction.Meanwhile, in the image area B, the image gravity center is not movedbecause the pixel position is located at an ideal position. As a result,as shown in FIG. 16C, it is understood that the image density isdecreased in the image area A as compared to that of the image area B,and a density change occurs.

As described above, in the case of performing processing of shiftingimage data by adding image data, there is a problem in that the movementamount also changes due to a change in developing threshold value, andhence banding correction cannot be performed satisfactorily. Such changein developing threshold value is liable to occur due to a change inimage forming conditions (e.g., a charging voltage for charging aphotosensitive drum, a developing voltage applied between aphotosensitive drum and a developing device, and an exposure lightintensity from a light scanning device). The embodiments of the presentinvention will be described in detail below in an illustrative mannerwith reference to the drawings. A direction of an axis of rotation of aphotosensitive drum, which is a direction in which scanning is performedwith a laser beam, is defined as a main scanning direction which is asecond direction, and a rotational direction of the photosensitive drum,which is a direction substantially orthogonal to the main scanningdirection, is defined as a sub-scanning direction which is a firstdirection.

First Embodiment

<Overall Configuration of Image Forming Apparatus>

FIG. 1A is a schematic cross-sectional view of a digital full-colorprinter (color image forming apparatus) configured to perform imageformation by using toners of a plurality of colors. An image formingapparatus 100 according to a first embodiment will be described withreference to FIG. 1A. The image forming apparatus 100 includes fourimage forming portions (image forming units) 101Y, 101M, 101C, and 101Bk(broken line portions) respectively configured to form images ofdifferent colors. The image forming portions 101Y, 101M, 101C, and 101Bkform images by using toners of yellow, magenta, cyan, and black,respectively. Reference symbols Y, M, C, and Bk denote yellow, magenta,cyan, and black, respectively, and suffixes Y, M, C, and Bk are omittedin the description below unless a particular color is described.

The image forming portions 101 each include a photosensitive drum 102,being a photosensitive member. A charging device 103, a light scanningdevice 104, and a developing device 105 are arranged around each of thephotosensitive drums 102. A cleaning device 106 is further arrangedaround each of the photosensitive drums 102. An intermediate transferbelt 107 of an endless belt type is arranged under the photosensitivedrums 102. The intermediate transfer belt 107 is stretched around adrive roller 108 and driven rollers 109 and 110, and rotates in adirection of an arrow B (clockwise direction) illustrated in FIG. 1Awhile forming an image. Further, primary transfer devices 111 arearranged at positions opposed to the photosensitive drums 102 across theintermediate transfer belt 107 (intermediate transfer member). The imageforming apparatus 100 according to the embodiment further includes asecondary transfer device 112 configured to transfer the toner image onthe intermediate transfer belt 107 onto a sheet S being a recordingmedium and a fixing device 113 configured to fix the toner image on thesheet S.

An image forming process from a charging step to a developing step ofthe image forming apparatus 100 will be described. The image formingprocess is the same in each of the image forming portions 101, and hencethe image forming process will be described with reference to an exampleof the image forming portion 101Y. Accordingly, descriptions of theimage forming processes in the image forming portions 101M, 101C, and101Bk are omitted. The charging device 103Y of the image forming portion101Y applies a uniform voltage to the photosensitive drum 102Y, tothereby charge the photosensitive drum 102Y that is driven to rotate inthe arrow direction (counterclockwise direction) illustrated in FIG. 1A.The charged photosensitive drum 102Y is exposed by a laser beam emittedfrom the light scanning device 104Y, which is indicated by the dasheddotted line. With this operation, an electrostatic latent image isformed on the rotating photosensitive drum 102Y (on the photosensitivemember). The electrostatic latent image formed on the photosensitivedrum 102Y receives toner adhered thereon through application of adeveloping voltage by the developing device 105Y, and is developed as atoner image of yellow. The same step is performed also in the imageforming portions 101M, 101C, and 101Bk.

The image forming process from a transfer step will be described. Theprimary transfer devices 111 applied with a transfer voltage transfertoner images of yellow, magenta, cyan, and black formed on thephotosensitive drums 102 of the image forming portions 101 onto theintermediate transfer belt 107. With this, the toner images ofrespective colors are superimposed one on another on the intermediatetransfer belt 107. That is, the toner images of four colors aretransferred onto the intermediate transfer belt 107 (primary transfer).The toner images of four colors transferred onto the intermediatetransfer belt 107 are transferred onto the sheet S conveyed from amanual feed cassette 114 or a sheet feed cassette 115 to a secondarytransfer portion by the secondary transfer device 112 (secondarytransfer). Then, the unfixed toner images on the sheet S are heated andfixed onto the sheet S by the fixing device 113, to thereby form afull-color image on the sheet S. The sheet S having the image formedthereon is delivered to a delivery portion 116. A density sensor 602serving as a density detection unit is configured to detect density of adensity patch formed on the intermediate transfer belt 107.

<Photosensitive Drum and Light Scanning Device>

FIG. 1B is an illustration of configurations of the photosensitive drum102, the light scanning device 104, and a controller for the lightscanning device 104. The light scanning device 104 includes a laserlight source 201, a collimator lens 202, a cylindrical lens 203, and arotary polygon mirror 204. The laser light source 201 includes aplurality of light emitting points. The plurality of light emittingpoints are each configured to emit a laser beam (light beam). Thecollimator lens 202 is configured to collimate the laser beam. Thecylindrical lens 203 condenses the laser beam having passed through thecollimator lens 202 in a sub-scanning direction. In the embodiment, thelaser light source 201 is described by exemplifying a light source inwhich a plurality of light emitting points are arranged, but issimilarly operated also in the case of using a single light source. Thelaser light source 201 is driven by a laser drive circuit 304. Therotary polygon mirror 204 is formed of a motor portion configured to beoperated to rotate and a reflection mirror mounted on a motor shaft. Aface of the reflection mirror of the rotary polygon mirror 204 ishereinafter referred to as “mirror face”. The rotary polygon mirror 204is driven by a mirror drive portion 305. The light scanning device 104includes fθ lenses 205 and 206 configured to receive a laser beam(scanning light) deflected by the rotary polygon mirror 204. Further,the light scanning device 104 includes a memory (storage unit) 302configured to store various pieces of information.

Further, the light scanning device 104 includes a beam detector 207(hereinafter referred to as “BD 207”) that is a signal generating unitconfigured to detect the laser beam deflected by the rotary polygonmirror 204 and output a horizontal synchronization signal (hereinafterreferred to as “BD signal”) in accordance with the detection of thelaser beam. The laser beam output from the light scanning device 104scans the photosensitive drum 102. The scanning direction of the laserbeam is substantially parallel to the rotary shaft of the photosensitivedrum 102. Every time the mirror face of the rotary polygon mirror 204scans the photosensitive drum 102, the light scanning device 104 causesa laser beam emitted from the laser light source to scan thephotosensitive drum 102 in the main scanning direction, to thereby formscanning lines corresponding to the number of laser elementssimultaneously. In the embodiment, a configuration is described in whichthe rotary polygon mirror 204 has five mirror faces, and the laser lightsource 201 includes eight laser elements, as an example. That is, in theembodiment, an image of eight lines is formed with one scanning, and therotary polygon mirror 204 scans the photosensitive drum 102 five timesper revolution of the rotary polygon mirror 204, to thereby form animage of forty lines in total.

The photosensitive drum 102 includes a rotary encoder 301 serving as aspeed detection unit on the rotary shaft, and the rotation speed of thephotosensitive drum 102 is detected with use of the rotary encoder 301.The rotary encoder 301 generates 1,000 pulses per revolution of thephotosensitive drum 102, and outputs information on the rotation speed(rotation speed data) of the photosensitive drum 102 based on theresults obtained by measuring a time interval between the generatedpulses with use of a built-in timer to a CPU 303. A known speeddetection technology other than the above-mentioned rotary encoder 301may be used as long as the rotation speed of the photosensitive drum 102can be detected. As a method other than the use of the rotary encoder301, there is given, for example, a configuration to detect the surfacespeed of the photosensitive drum 102 with a laser Doppler.

Further, the image forming apparatus 100 includes a thermistor 401serving as a temperature detection unit configured to detect an internaltemperature of the image forming apparatus 100, and the CPU 303 receivesa temperature detection signal from the thermistor 401. The CPU 303 isconfigured to control the image forming conditions in accordance withthe temperature in the image forming apparatus 100 detected by thethermistor 401 so that image density reaches predetermined density inadvance. In the embodiment, the image forming conditions refer to acharging voltage of the charging device 103 configured to charge thephotosensitive drum 102 and a developing voltage applied by thedeveloping device 105 so as to develop an electrostatic latent image onthe photosensitive drum 102. Further, in the embodiment, the imageforming condition refers to an exposure light intensity from the lightscanning device 104 configured to form an electrostatic latent image onthe photosensitive drum 102. An example of controlling the image formingcondition with use of a developing voltage will be described below. TheCPU 303 is configured to finely adjust the image forming conditions toadjust the image density with high accuracy based on the densitydetection results of a patch formed on the intermediate transfer belt107 detected by the density sensor 602. Further, the CPU 303 also finelyadjusts an exposure amount based on the density detection value of thepatch detected by the density sensor 602.

The charging device 103 is configured to apply a charging voltage to thephotosensitive drum 102 with an output voltage from a charging voltagedrive circuit (not shown). The CPU 303 is configured to set a value ofvoltage to be output to the charging device 103, with respect to thecharging voltage drive circuit. Similarly, the developing device 105also applies a developing voltage to the photosensitive drum 102 with anoutput voltage from a developing voltage drive circuit (not shown). TheCPU 303 is configured to set a value of voltage to be output to thedeveloping device 105, with respect to the developing voltage drivecircuit. Further, the CPU 303 instructs the laser drive circuit 304 onan emission light intensity of the laser light source 201, to therebyadjust an exposure amount with respect to the photosensitive drum 102.

<Function of Controller for Light Scanning Device>

Next, the CPU 303 serving as the controller for the light scanningdevice 104 and a clock signal generating portion 308 will be describedwith reference to FIG. 2. The CPU 303 and the clock signal generatingportion 308 are mounted on the image forming apparatus 100. FIG. 2 is ablock diagram for illustrating the functions of the CPU 303 configuredto execute correction processing of correcting distortion and unevenimage density of an image described later. The CPU 303 includes afiltering portion 501, an error diffusion processing portion 502, and apulse width modulation (PWM) signal generating portion 503. Thefiltering portion 501 is configured to perform filtering by subjectinginput image data to a convolution operation. The error diffusionprocessing portion 502 is configured to subject the image data after thefiltering to error diffusion processing. The PWM signal generatingportion 503 is configured to subject the image data (density data) afterthe error diffusion processing to PWM transformation and output a PWMsignal to the laser drive circuit 304 of the light scanning device 104.The clock signal generating portion 308 is configured to output a clocksignal CLK(1) and a clock signal CLK(2) to the CPU 303. The clock signalCLK(1) is a clock signal illustrated in FIG. 5 described later. Theclock signal CLK(1) is a signal generated by multiplying the clocksignal CLK(2). Thus, the clock signal CLK(1) and the clock signal CLK(2)have a synchronization relationship. In the embodiment, the clock signalgenerating portion 308 outputs the clock signal CLK(1) generated bymultiplying the clock signal CLK(2) by 16 to the CPU 303. The clocksignal CLK(2) is a signal having a period corresponding to one pixel.The clock signal CLK(1) is a signal having a period corresponding todivided pixels obtained by dividing one pixel by 16.

Further, the CPU 303 includes a filter coefficient setting portion 504,a filter function output portion 505, and a correction value settingportion 506. The filter function output portion 505 is configured tooutput data on a function to be used for a convolution operation (forexample, data in a table) to the filter coefficient setting portion 504.As a function to be used for the convolution operation, there is given,for example, linear interpolation and bicubic interpolation. Thecorrection value setting portion 506 is configured to identify a mirrorface which reflects a laser beam from among a plurality of mirror facesbased on a face synchronization signal input from a face identifyingportion 507. The correction value setting portion 506 is configured todetermine a positional deviation amount in the rotation direction of thephotosensitive drum 102 of a scanning line formed with a laser beamdeflected by the mirror face identified by the face identifying portion507 described later. The correction value setting portion 506 thencalculates a correction value based on the positional deviation amountand outputs the calculated correction value to the filter coefficientsetting portion 504. The filter coefficient setting portion 504 isconfigured to calculate a filter coefficient to be used for thefiltering in the filtering portion 501 based on information on theconvolution function input from the filter function output portion 505and the correction value input from the correction value setting portion506. The filter coefficient setting portion 504 is configured to set thecalculated filter coefficient in the filtering portion 501. Thecorrection value input to the filter coefficient setting portion 504from the correction value setting portion 506 is a correction value setindividually for each of the plurality of mirror faces.

Further, the CPU 303 includes the face identifying portion 507. The faceidentifying portion 507 is configured to identify a mirror face of therotary polygon mirror 204 based on an HP signal input from a homeposition sensor (hereinafter referred to as “HP sensor”) 307 of thelight scanning device 104 and the BD signal input from the BD 207. Theface identifying portion 507 is configured to output information of theidentified mirror face to the correction value setting portion 506 as aface synchronization signal.

As illustrated in FIG. 1B, the CPU 303 is configured to receive imagedata from an image controller (not shown) configured to generate imagedata. The image data is gradation data indicating a density value. Thegradation data is data of a plurality of bits indicating a density valuefor each pixel. For example, in the case of image data of 4 bits, adensity value of one pixel is expressed by 16 gradations, and in thecase of image data of 8 bits, a density value of one pixel is expressedby 256 gradations. In the embodiment, the image data input to the CPU303 from the image controller is 4 bits per pixel. The filtering portion501 is configured to subject the image data to filtering for each pixelin synchronization with the clock signal CLK(2). The CPU 303 isconnected to the rotary encoder 301, the BD 207, the memory 302, thelaser drive circuit 304, and the rotary polygon mirror drive portion(hereinafter referred to as “mirror drive portion”) 305. The CPU 303 isconfigured to detect a write position of a scanning line based on the BDsignal input from the BD 207 and count a time interval of the BD signal,to thereby detect the rotation speed of the rotary polygon mirror 204.Further, the CPU 303 is configured to output an acceleration ordeceleration signal for designating acceleration or deceleration to themirror drive portion 305 so that the rotary polygon mirror 204 reaches apredetermined speed. The mirror drive portion 305 is configured tosupply a driving current to the motor portion of the rotary polygonmirror 204 in accordance with the acceleration or deceleration signalinput from the CPU 303, to thereby drive a motor 306.

As illustrated in FIG. 2, the HP sensor 307 is mounted on the rotarypolygon mirror 204 and is configured to output the HP signal to the CPU303 at timing at which the rotary polygon mirror 204 reaches apredetermined angle during a rotation operation. For example, the HPsignal is generated once during every rotation of the rotary polygonmirror 204. The face identifying portion 507 resets an internal counterin response to the generation of the HP signal. Then, the faceidentifying portion 507 increments a count value of the internal counterby “1” every time the BD signal is input. That is, each count value ofthe internal counter is information indicating a corresponding one ofthe plurality of mirror faces of the rotary polygon mirror 204. The CPU303 can identify which of the plurality of mirror faces the input imagedata corresponds to with use of the count value. That is, the CPU 303can switch a filter coefficient for correcting the input image data withuse of the count value.

The memory 302 is configured to store, for each mirror face, positioninformation (first scanning position information) indicating positionaldeviation amounts from ideal scanning positions in the sub-scanningdirection of a plurality of laser beams reflected by the mirror faces ofthe rotary polygon mirror 204. Further, the memory 302 is configured tostore position information (second scanning position information)indicating a positional deviation amount from the ideal scanningposition in the sub-scanning direction of the laser beam emitted fromeach light emitting point. The CPU 303 is configured to read each of thefirst scanning position information and the second scanning positioninformation. The CPU 303 is configured to calculate the position of eachscanning line based on the position information read from the memory 302and calculate image data taking information for correcting the positionof each scanning line into account from the calculated position of eachscanning line and the input image data. The PWM signal generatingportion 503 of the CPU 303 is configured to convert the image datataking the information for correcting the position of each scanning lineinto account into drive data. A ROM 309 is configured to store aconversion table for converting image data of 4 bits into drive data of16 bits as shown in FIG. 17. A vertical axis of the conversion tableshown in FIG. 17 represents image data indicating density values of 4bits, which corresponds to one pixel. A horizontal axis of theconversion table shown in FIG. 17 represents drive data of 16 bitsassociated with the density values of 4 bits individually. For example,in the case where image data input to the PWM signal generating portion503 is a bit pattern of “0110”, the PWM signal generating portion 503converts the image data “0110” into drive data that is a bit pattern of“0000000001111111” with use of the conversion table. The PWM signalgenerating portion 503 outputs the converted drive data in the order of“0000000001111111” serially on a bit basis in accordance with the clocksignal (1) described later. When the PWM signal generating portion 503outputs the drive data, a PWM signal is generated. When the PWM signalgenerating portion 503 outputs “1”, a light emitting point emits a laserbeam. When the PWM signal generating portion 503 outputs “0”, a lightemitting point does not output a laser beam.

<Scanning Position Information>

Next, scanning position information stored in the memory 302 will bedescribed with reference to FIG. 3 and Table 1.

FIG. 3 is an illustration of a state of positional deviation of eachscanning line from an ideal position. Scanning lines scanned by eachlaser beam of the laser light source having eight light emitting pointsare denoted by LD1, LD2, LD3, LD4, LD5, LD6, LD7, and LD8. An idealinterval between the respective scanning lines is determined based on aresolution. For example, in the case of an image forming apparatushaving a resolution of 1,200 dpi, an ideal interval between therespective scanning lines is 21.16 μm. When the scanning line LD1 isdefined as a reference position, ideal distances D2 to D8 of thescanning lines LD2 to LD8 from the scanning line LD1 are calculated byExpression (1).Dn=(n−1)×21.16 μm (n=2 to 8)  Expression (1)For example, the ideal distance D4 from the scanning line LD1 to thescanning line LD4 is 63.48 μm (=(4−1)×21.16 μm).

In this case, an interval between the scanning lines on thephotosensitive drum 102 has an error due to an error of arrangementintervals of the plurality of light emitting points and characteristicsof a lens. The positional deviation amounts of the scanning linepositions of the scanning lines LD2 to LD8 with respect to idealpositions determined based on the ideal distances D2 to D8 are denotedby X1 to X7. Regarding the first face of the rotary polygon mirror 204,for example, the positional deviation amount X1 of the scanning line LD2is defined as a difference between the ideal position of the scanningline LD2 (hereinafter referred to as “LINE 2”, which similarly appliesto the other scanning lines) and the actual scanning line. Further, forexample, the positional deviation amount X3 of the scanning line LD4 isdefined as a difference between the LINE 4 and the actual scanning line.

Due to a variation in manufacturing of each mirror face of the rotarypolygon mirror 204, the mirror faces of the rotary polygon mirror 204are not completely parallel to the rotary shaft, and the rotary polygonmirror 204 has an angle variation for each mirror face. The positionaldeviation amounts with respect to the ideal positions in each mirrorface of the rotary polygon mirror 204 are denoted by Y1 to Y5 when thenumber of the mirror faces of the rotary polygon mirror 204 is five. InFIG. 3, a deviation amount of the scanning line LD1 from the idealposition (LINE 1) in the first face of the rotary polygon mirror 204 isdenoted by Y1, and a deviation amount of the scanning line LD1 from theideal position (LINE 9) in the second face of the rotary polygon mirror204 is denoted by Y2.

A mirror face of the rotary polygon mirror 204 is defined as an m-thface, and a positional deviation amount of a scanning line (LDn) by ann-th laser beam from the laser light source is denoted by Zmn. Then, thepositional deviation amount Zmn is represented by Expression (2) withuse of the positional deviation amounts X1 to X7 of each scanning lineand the positional deviation amounts Y1 to Y5 of each mirror face.Zmn=Ym+X(n−1) (m=1 to 5, n=1 to 8)  Expression (2)where X(0)=0For example, a positional deviation amount Z14 regarding the scanningline LD4 in the first face of the rotary polygon mirror 204 isdetermined to be Z14=Y1+X3 by Expression (2). Further, a positionaldeviation amount Z21 regarding the scanning line LD1 in the second faceof the rotary polygon mirror 204 is determined to be Z21=Y2 byExpression (2).

When the positional deviation amount Zmn is calculated by Expression(2), it is only necessary that the number of pieces of data to be usedfor calculating the positional deviation amount Zmn correspond to thenumber of the mirror faces of the rotary polygon mirror 204 and thenumber of light emitting points of the laser light source. An addressmap of positional deviation data stored in the memory 302 is shown inTable 1.

TABLE 1 Address Data 0 LD2 Position Information X1 1 LD3 PositionInformation X2 2 LD4 Position Information X3 3 LD5 Position InformationX4 4 LD6 Position Information X5 5 LD7 Position Information X6 6 LD8Position Information X7 7 First Face Position Information Y1 8 SecondFace Position Information Y2 9 Third Face Position Information Y3 10Fourth Face Position Information Y4 11 Fifth Face Position InformationY5

As shown in Table 1, information on the respective positional deviationamounts (described as position information) X1 to X7 of the scanningline LD2 to the scanning line LD8 is stored in from an address 0 to anaddress 6 of the memory 302. Further, information on the respectivepositional deviation amounts Y1 to Y5 of the first face to the fifthface of the mirror faces of the rotary polygon mirror 204 is stored infrom an address 7 to an address 11 of the memory 302. In the embodiment,description is given on the assumption that the eight scanning lines ofeach laser beam are deviated uniformly due to the positional deviationof each mirror face of the rotary polygon mirror 204. That is, in theembodiment, twelve pieces of position information are stored in thememory 302. However, when there is a variation in positional deviationamount of each scanning line of a laser beam for each mirror face of therotary polygon mirror 204, there may be stored information on apositional deviation amount only for a combination of each mirror faceof the rotary polygon mirror 204 and each scanning line of the laserbeam. That is, in this case, forty pieces of position information arestored in the memory 302 with the number of the mirror faces of therotary polygon mirror 204 being five, and the number of light emittingpoints of the laser light source being eight.

(Memory Storage Operation)

As information on a positional deviation amount to be stored in thememory 302, for example, data measured at the time of adjustment of thelight scanning device 104 in a factory or the like is stored. Further,the image forming apparatus 100 may include a position detection unitconfigured to detect the position of a scanning line scanned with alaser beam emitted from the laser light source 201 so that theinformation stored in the memory 302 may be updated in real time. As theposition detection unit configured to detect a position of scanninglight in the sub-scanning direction, a known technology may be used. Forexample, a position may be detected by a CMOS sensor or a positionsensitive detector (PSD) arranged in the light scanning device 104 orarranged on a scanning path of a laser beam near the photosensitive drum102. Further, a triangular slit may be formed in a surface of a photodiode (PD) arranged in the light scanning device 104 or arranged nearthe photosensitive drum 102, to thereby detect a position from an outputpulse width of the PD.

FIG. 4 is a block diagram for illustrating a step of storing informationin the memory 302 of the light scanning device 104 in a factory or thelike as an example. The same configurations as those of FIG. 2 aredenoted by the same reference symbols as those therein, and thedescription thereof is omitted. At the time of adjustment of the lightscanning device 104, a measuring instrument 400 is arranged at aposition corresponding to the scanning position on the photosensitivedrum 102 when the light scanning device 104 is mounted on the imageforming apparatus 100. The measuring instrument 400 includes a measuringportion 410 and a calculation portion 402, and the calculation portion402 is configured to receive a face synchronization signal from the faceidentifying portion 507 of the CPU 303 of FIG. 2. In the CPU 303 of FIG.4, only the face identifying portion 507 is illustrated. First, a laserbeam is radiated to the measuring portion 410 from the light scanningdevice 104. The measuring portion 410 includes a triangular slit 411 anda PD 412. A laser beam emitted from the light scanning device 104indicated by the arrow with the alternate long and short dash line inFIG. 4 scans the triangular slit 411. The measuring portion 410 measuresthe position in the sub-scanning direction of a scanning line based oninformation on the laser beam input to the PD 412 through the triangularslit 411. The measuring portion 410 outputs information on the measuredposition in the sub-scanning direction of the scanning line in eachmirror face (hereinafter referred to as “data for each face”) of therotary polygon mirror 204 to the calculation portion 402.

Meanwhile, the face identifying portion 507 is configured to receive theHP signal from the HP sensor 307 of the light scanning device 104 andreceive the BD signal from the BD 207. With this, the face identifyingportion 507 is configured to identify a mirror face of the rotarypolygon mirror 204 and output information on the identified mirror faceto the calculation portion 402 as a face synchronization signal. Thecalculation portion 402 is configured to write the information on theposition in the sub-scanning direction of the scanning line measured bythe measuring portion 410 into an address on the memory 302 of the lightscanning device 104 in accordance with the information on the mirrorface of the rotary polygon mirror 204 input from the face identifyingportion 507. Thus, the information on the positional deviation amountsof the scanning lines caused by a variation in intervals between theeight light emitting points of the laser light source 201 (X1 to X7) andthe information on the positional deviation amounts of the scanninglines caused by an optical face tangle error of the mirror face of therotary polygon mirror 204 (Y1 to Y5) are stored in the memory 302.

<Calculation Method for Positional Deviation Amount>

FIG. 5 is an illustration of control timing in one scanning period of alaser beam in the embodiment. (1) represents a CLK signal correspondingto a pixel period per divided pixel ( 1/16 pixel) obtained by dividingone pixel by 16, and (2) represents input timing of the BD signal fromthe BD 207 to the CPU 303. (3) and (4) are each an illustration oftiming at which the CPU 303 outputs drive data (DATA1, DATA2, etc.). (4)represents drive data after the filtering.

With the BD signal output from the BD 207 being a reference, during aperiod of time from timing at which the BD signal is input to the CPU303 to timing at which a subsequent BD signal is input to the CPU 303, aperiod of time from timing at which the BD signal is input to the CPU303 to timing at which the processing of the image data input to the CPU303 is started is defined as T1. Further, during the period of time fromtiming at which the BD signal is input to the CPU 303 to timing at whicha subsequent BD signal is input to the CPU 303, a period of time fromtiming at which the BD signal is input to the CPU 303 to timing at whichthe output of the image data input to the CPU 303 is completed isdefined as T2. After the BD signal is input to the CPU 303, the CPU 303stands by until the predetermined period of time T1 elapses. Then, theCPU 303 starts the filtering of the input image data in synchronizationwith the clock signal CLK(2) to generate drive data successively fromthe processed image data and output the drive data on a bit basis, tothereby output the PWM signal to the laser drive circuit 304. Then,after the predetermined period of time T2 elapses from the input of theBD signal, the CPU 303 finishes the processing of the image data in onescanning line. The CPU 303 calculates, for each scanning, a positionaldeviation amount of the scanning line in the scanning period until thepredetermined period of time T1 elapses from the detection of the BDsignal, that is, while the laser beam scans a non-image area. Then, theCPU 303 causes the filter coefficient setting portion 594 to set afilter coefficient based on the calculated positional deviation amount.Then, the CPU 303 causes, for each scanning, the filtering portion 501to correct the image data with use of the filter coefficient set by thefilter coefficient setting portion 504 until the predetermined period oftime T2 elapses from the elapse of the predetermined period of time T1.

(Calculation of Positional Deviation Amount Taking Uneven Speed ofPhotosensitive Drum into Account)

Next, processing of calculating a positional deviation amount of ascanning line will be described. FIG. 6 is a flowchart for illustratingprocessing performed by the CPU 303 to calculate a positional deviationamount during image formation. The CPU 303 is configured to perform thecontrol illustrated in FIG. 6 once per scanning, to thereby calculate apositional deviation amount before the predetermined period of time T1elapses from the detection of the BD signal. The CPU 303 is assumed toinclude a timer for measuring a time. In Step S7002, the CPU 303determines whether or not the BD signal has been input from the BD 207.When the CPU 303 determines that the BD signal has been input (YES inS7002), the CPU 303 stops a timer (not shown) measuring a time intervalof the BD signal, reads a timer value, and stores the timer value in aninternal register. Then, in order to measure a time interval up toreception of the next BD signal, the CPU 303 resets and starts the timer(not shown) and proceeds to processing in Step S7003. In the case wherethe CPU 303 includes two or more timers (not shown), different timersmay be used alternately every time the BD signal is received, to therebymeasure a time interval. Further, in this case, the measured timeinterval of the BD signal is stored in the internal register of the CPU303, but the measured time interval may be stored in, for example, a RAM(not shown) serving as an internal storage portion of the CPU 303. Whenthe CPU 303 determines that the BD signal has not been input (NO inS7002), the CPU 303 repeats the control in Step S7002 so as to wait forthe input of the BD signal.

In Step S7003, the CPU 303 reads rotation speed data of thephotosensitive drum 102 from the rotary encoder 301. In Step S7004, theCPU 303 calculates a printing speed Vpr based on the time interval ofthe BD signal stored in the internal register. The printing speed Vpr iscalculated by dividing a value, which is obtained by multiplying thenumber of beams of the laser light source 201 by the interval of thescanning lines, by ΔT (time interval of the BD signal). For example, inthe case of the embodiment, the number of beams is eight, and theinterval of the scanning lines is 21.16 μm (resolution: 1,200 dpi), andhence Vpr=(8×21.16 μm)/ΔT is satisfied. A rotation speed Vp of therotary polygon mirror 204 has a proportional relationship with theprinting speed Vpr, and hence can be determined from the calculatedprinting speed Vpr. In Step S7005, the CPU 303 calculates a positionaldeviation amount A based on the rotation speed of the photosensitivedrum 102 read in Step S7003 and the rotation speed of the rotary polygonmirror 204 calculated in Step S7004. A calculation method for thepositional deviation amount A will be described in detail later.

In Step S7006, the CPU 303 reads face information (Y1 to Y5 in Table 1)and beam position information (X1 to X7 in Table 1) of the rotarypolygon mirror 204 from the memory 302. In Step S7007, the CPU 303calculates a positional deviation amount B (=Zmn) with use of Expression(2) based on the face information and the beam position information readin Step S7006. In Step S7008, the CPU 303 adds up the positionaldeviation amount A calculated in Step S7005 and the positional deviationamount B calculated in Step S7007, to thereby calculate a sum (totalvalue) of the positional deviation amounts. In Step S7009, the CPU 303stores the total positional deviation amount calculated in Step S7008 inthe internal register of the CPU 303. In this case, the positionaldeviation amount stored in the internal register is read and used forcalculation at a time of the filtering described above.

(Calculation of Positional Deviation Amount)

An expression for calculation of the positional deviation amount A bythe CPU 303 in Step S7005 will be described in detail. When the rotationspeed of the photosensitive drum 102 is denoted by Vd, the rotationspeed of the rotary polygon mirror 204 is denoted by Vp, and onescanning period is denoted by ΔT (see FIG. 5), the positional deviationamount A caused by a speed difference between the rotation speed Vd ofthe photosensitive drum 102 and the rotation speed Vp of the rotarypolygon mirror 204 is calculated by Expression (3).A=(Vd−Vp)×ΔT  Expression (3)

In Expression (3), ΔT represents a period of time corresponding to aninterval of output timing of the BD signal, and the positional deviationamount A represents a positional deviation amount of scanning lines thatmove during one scanning period due to the difference between therotation speed Vd of the photosensitive drum 102 and the rotation speedVp of the rotary polygon mirror 204. As described above, the rotationspeed Vp of the rotary polygon mirror 204 is determined based on theprinting speed Vpr. Then, the printing speed Vpr is determined based onthe relationship between the one scanning period ΔT and the number oflight emitting points (the light emitting points are eight in theembodiment) by Expressions (4) and (5).Vp=Number of beams×21.16/ΔT  Expression (4)ΔT=1/(Number of mirror faces of rotary polygon mirror 204×Number ofrevolutions per second of rotary polygon mirror 204)  Expression (5)

When the positional deviation caused by an uneven speed of thephotosensitive drum 102 of the n-th scanning line from the referenceposition in the sub-scanning direction is denoted by An, the positionaldeviation in the sub-scanning direction is represented by anaccumulation of the positional deviation of each scanning. Further, whenthe positional deviation amount based on the face information of therotary polygon mirror 204 of the n-th scanning line from the referenceposition in the sub-scanning direction and the beam information isdenoted by Bn, the position y in the sub-scanning direction of the n-thscanning line is represented by Expression (6).

$\begin{matrix}{y = {n + \left( {B_{n} + {\sum\limits_{p = 1}^{n}A_{p}}} \right)}} & {{Expression}\mspace{14mu}(6)}\end{matrix}$

The value “y” on the left side of Expression (6) is defined only when“n” is an integer. That is, the value “y” is a discrete function.However, in the embodiment, each value “y” determined from an integer isinterpolated by linear interpolation and handled as a continuousfunction y=ft(n) as described later. In the embodiment, linearinterpolation is used so as to simplify hardware, but interpolation ofthe function may be performed by other methods such as Lagrangeinterpolation and spline interpolation.

When the pixel positions in the sub-scanning direction of pixel numbersn0 and n0+1 in the embodiment are denoted by y_(n0) and y_(n0+1), anexpression of conversion into the continuous function within a range offrom the pixel position y_(n0) to the pixel position y_(n0+1) in thesub-scanning direction is given below.y=y _(n0)×(1−n+n0)+y _(n0+1)×(n−n0)  Expression (7)

The processing of FIG. 6 is performed once per scanning, that is, oncefor eight beams (eight scanning lines). Therefore, in Steps S7006 toS7008, the positional deviation amounts of the eight beams arecollectively calculated, and all the calculated positional deviationamounts of the eight beams are stored in Step S7009. Further, in theembodiment, the rotation speed data of the photosensitive drum 102 isobtained in real time from the rotary encoder 301 and fed back topositional deviation correction. However, a profile of speed fluctuationdata measured in advance may be stored in the memory 302, and positionaldeviation may be corrected in accordance with the stored profile.Further, when positional deviation information is obtained in real time,the positional deviation information may be used as it is for correctionof the positional deviation although control is delayed. In this case,in order to prevent the influence due to the delayed control, aparticular frequency component, e.g., a high-frequency component of afluctuation amount of positional deviation may be filtered to be usedfor correction.

Then, in the embodiment, a filter operation described later is performedbased on the image data and the positional deviation amounts of aplurality of scanning lines. Therefore, in the above-mentionedpositional deviation amount calculation operation, the CPU 303 isconfigured to determine positional deviation amounts of a plurality ofscanning lines to be used in the filter operation during a period inwhich the period of time T1 elapses from the output of the BD signalfrom the BD 207. For example, when the range of the filter operation isdefined as L=3, image data on three pixels above and below a line ofinterest is referred to, and a positional deviation amount of eachscanning line within the range of the three pixels above and below theline of interest is calculated, to thereby perform the filter operation.

In this case, the positional deviation amount of the scanning linecorresponding to the line of interest is calculated during a periodimmediately before image formation. Further, the calculation results ofthe positional deviation amounts calculated before are used for thescanning lines scanned before the scanning line of interest. For ascanning line to be scanned at timing after the scanning line ofinterest, a positional deviation amount B is determined based on theface information of the rotary polygon mirror 204 corresponding to thenext scanning line and the beam position information. Further, arotation speed Vp of the rotary polygon mirror 204 and a rotation speedVd of the photosensitive drum 102 are determined by predicting eachspeed in a next scanning line based on a value detected at previousscanning timing and a value detected at current scanning timing. Thedetails of the calculation method for a positional deviation amount willbe described later.

<Method for Filter Operation of Image Data>

In the embodiment, the CPU 303 is configured to perform processing ofcorrecting image data through a filter operation based on the positionaldeviation amounts in the sub-scanning direction of the scanning linesformed by laser beams and output drive data generated based on thecorrected image data to the laser drive circuit 304. The filteroperation is specifically an operation of performing convolutionprocessing, and in the embodiment, the convolution processing isperformed based on the image data and the positional deviation amount.Now, the filter operation will be described with reference to aflowchart of FIG. 7. FIG. 7 is a flowchart for illustrating a filteroperation for correcting uneven image density and banding caused by thepositional deviation in the sub-scanning direction. In Step S3602, theCPU 303 reads a positional deviation amount in the sub-scanningdirection. Specifically, the CPU 303 reads a positional deviation amountstored in the internal register in Step S7009 of FIG. 6. In theembodiment, a pixel position in the sub-scanning direction of inputimage data is corrected based on the positional deviation amount in thesub-scanning direction, followed by the filtering, to thereby outputimage data, that is, density. The convolution processing according tothe embodiment is the processing involving correcting sparseness anddenseness of density in the sub-scanning direction caused by deviationof a scanning line in the sub-scanning direction by moving a pixel ofinterest in the sub-scanning direction in accordance with the deviationof the scanning line. The convolution processing is processing involvingcorrecting the sparseness and denseness of density by causing a pixelvalue of the pixel of interest to be output or not to be outputdepending on the movement in the sub-scanning direction.

(State of Positional Deviation of Scanning Line)

The state of positional deviation of a scanning line can be roughlyclassified into four cases. First, regarding the state of positionaldeviation, there is a case (a) in which the position of a scanning line(hereinafter referred to as “scanning position”) on the photosensitivedrum 102 is shifted in an advance direction with respect to an idealscanning position, and a case (b) in which the scanning position on thephotosensitive drum 102 is shifted in a return direction with respect tothe ideal scanning position. Further, regarding the state of positionaldeviation, there is a case (c) in which the scanning positions on thephotosensitive drum 102 are dense with respect to the ideal scanningpositions, and a case (d) in which the scanning positions on thephotosensitive drum 102 are sparse with respect to the ideal scanningpositions. Specific examples of the state of positional deviation in thesub-scanning direction are illustrated in FIG. 8A, FIG. 8B, FIG. 8C, andFIG. 8D. In FIG. 8A to FIG. 8D, the broken lines represent scanningpositions, and in FIG. 8A to FIG. 8D, (1) to (5) represent the order ofscanning. In the embodiment, eight beams are used for scanningsimultaneously, but description is given on the assumption that theorder is allocated to each beam arranged successively in thesub-scanning direction. Each column on the left side of FIG. 8A to FIG.8D represents ideal scanning positions, and each column on the rightside thereof represents scanning positions on the photosensitive drum102. S1 to S5 represent positional deviation amounts from the idealscanning positions with respect to scanning numbers (1) to (5). The unitof a positional deviation amount is represented based on the case wherethe ideal beam interval (21.16 μm at 1,200 dpi) is defined as 1, and theadvance direction of a laser beam in the sub-scanning direction(hereinafter simply referred to as “advance direction”) is set to apositive value. Further, the return direction of the laser beam in thesub-scanning direction (hereinafter simply referred to as “returndirection”) is set to a negative value. Further, in order to describethe state of an image, each pixel arranged in the sub-scanning directionis represented by a circle on the scanning line. The shading of thecircle represents density.

FIG. 8A is an illustration of an example in which the scanning positionson the photosensitive drum 102 are shifted by 0.2 uniformly in theadvance direction from the ideal scanning positions. The positionaldeviation amount as illustrated in FIG. 8A is hereinafter referred to asa shift amount of +0.2. FIG. 8B is an illustration of an example inwhich the scanning positions on the photosensitive drum 102 are shiftedby 0.2 uniformly in the return direction from the ideal scanningpositions. The positional deviation amount as illustrated in FIG. 8B ishereinafter referred to as a shift amount of −0.2. In FIG. 8A and FIG.8B, the scanning positions are shifted uniformly, and hence the intervalbetween the scanning positions on the photosensitive drum 102 is 1 inboth the cases.

In FIG. 8C, the positional deviation amount is 0 at a predeterminedscanning position on the photosensitive drum 102. However, as thescanning position returns backward from the scanning position of thepositional deviation amount of 0, the positional deviation amount in theadvance direction increases, and as the scanning position proceedsforward from the scanning position of the positional deviation amount of0, the positional deviation amount in the return direction increases.For example, S3 is +0 in the scanning number (3), but S2 is +0.2 in thescanning number (2), S1 is +0.4 in the scanning number (1), S4 is −0.2in the scanning number (4), and S5 is −0.4 in the scanning number (5).In FIG. 8C, the interval between the scanning positions is 0.8, which issmaller than 1. The state of positional deviation as illustrated in FIG.8C is hereinafter referred to as being dense at an interval of a (1−0.2)line.

In FIG. 8D, the positional deviation amount is 0 at a predeterminedscanning position on the photosensitive drum 102. However, as thescanning position returns backward from the scanning position of thepositional deviation amount of 0, the positional deviation amount in thereturn direction increases, and as the scanning position proceedsforward from the scanning position of the positional deviation amount of0, the positional deviation amount in the advance direction increases.For example, S3 is +0 in the scanning number (3), but S2 is −0.2 in thescanning number (2), S1 is −0.4 in the scanning number (1), S4 is +0.2in the scanning number (4), and S5 is +0.4 in the scanning number (5).In FIG. 8D, the interval between the scanning positions is 1.2, which islarger than 1. The state of positional deviation as illustrated in FIG.8D is hereinafter referred to as being sparse at an interval of a(1+0.2) line.

In the dense state as illustrated in FIG. 8C, positional deviationoccurs, and in addition, the scanning positions are dense to causepixels to be arranged densely on the photosensitive drum 102, with theresult that a pixel value per predetermined area increases, to therebyincrease density. In contrast, in the sparse state as illustrated inFIG. 8D, positional deviation occurs, and in addition, the scanningpositions are sparse to cause pixels to be arranged sparsely on thephotosensitive drum 102, with the result that a pixel value perpredetermined area decreases, to thereby decrease density. In anelectrophotographic process, a shading difference may be furtheremphasized due to a relationship between the depth of a latent imagepotential and development characteristics. Further, when the dense orsparse state occurs alternately as illustrated in FIG. 8C and FIG. 8D, aperiodic shading causes moire, which is liable to be detected visuallyeven at the same amount depending on a space frequency.

Referring back to the flowchart of FIG. 7, in Step S3603, the CPU 303reads a setting value of a developing voltage applied by the developingdevice 105, which is set in the developing voltage drive circuit. InStep S3604, the CPU 303 generates attribute information for correctionof each pixel of an input image with the correction value settingportion 506. In the embodiment, the pixel position in the sub-scanningdirection of an input image is subjected to coordinate transformation inadvance and interpolated, thereby enabling correction of positionaldeviation and correction of local shading simultaneously whilemaintaining density of the input image. The attribute information forcorrection specifically refers to a correction value C described later.

(Coordinate Transformation)

A method for coordinate transformation according to the embodiment willbe described with reference to FIG. 9A, FIG. 9B, FIG. 10A, FIG. 10B,FIG. 10C, FIG. 10D, FIG. 11A, and FIG. 11B. In each graph of FIG. 9A toFIG. 11B, a horizontal axis represents a pixel number “n”, and avertical axis represents a pixel position (which is also a scanningposition) “y” (y′ after the coordinate transformation) in thesub-scanning direction, with the unit being a line. Further, FIG. 9A,FIG. 9B, FIG. 11A, and FIG. 11B correspond to FIG. 8A, FIG. 8B, FIG. 8C,and FIG. 8D, respectively. Each graph on the left side of FIG. 9A, FIG.9B, FIG. 11A, and FIG. 11B represents the state before the coordinatetransformation, and each graph on the right side thereof represents thestate after the coordinate transformation for the y-axis. Square dotsplotted in each graph represent scanning positions on the photosensitivedrum 102, and circular dots therein represent ideal scanning positions.

(Case of being Shifted in Advance Direction and Return Direction)

The graph on the left side of FIG. 9A will be first described. In thegraph before the coordinate transformation, at the ideal scanningpositions plotted with the circular dots, for example, a pixel position“y” in the sub-scanning direction is 2 with respect to the pixel number2. Thus, the y-coordinate of the pixel position “y” is equal to that ofthe pixel number “n”, and the ideal scanning positions are representedby a straight line (indicated by the alternate long and short dash line)with a gradient of 1. The straight line of the alternate long and shortdash line is represented by Expression (8).y=n  Expression (8)

As illustrated in FIG. 8A, the scanning positions plotted with thesquare dots are shifted by S (=0.2) line in the advance direction (+direction of y-axis) with respect to the ideal scanning positionsplotted with the circular dots. Therefore, the scanning positionsplotted with the square dots are represented by a straight line(indicated by the solid line) offset with the gradient being 1, which isrepresented by Expression (9).y=n+S  Expression (9)

In the embodiment, the coordinate transformation is performed so thatthe actual scanning positions are transformed into the ideal scanningpositions. Therefore, in the example illustrated in FIG. 9A, it is onlynecessary that the coordinate transformation be performed with use ofExpression (10). In Expression (10), C represents a correction amount.y′=y+C  Expression (10)Thus, the correction amount C is represented by a shift amount S andExpression (11).C=−S  Expression (11)

Through Expression (10) of the coordinate transformation and Expression(11) for determining the correction amount C, Expressions (8) and (9)are converted as represented by Expressions (12) and (13), respectively.y′=y+C=n+(−S)=n−S  Expression (12)y′=y+C=(n+S)+C=(n+S)+(−S)=n  Expression (13)

In FIG. 9B, when the shift amount S is defined as −0.2, Expression (13)similarly holds from Expression (8), and the similar description to thatof FIG. 9A can be given. As illustrated in FIG. 9A and FIG. 9B, when thescanning lines are not sparse or dense, and are shifted in the advancedirection or the return direction, a straight line has a predeterminedgradient before and after the coordinate transformation.

(Case in which Dense or Sparse State Occur)

Now, the coordinate transformation will be described, which is alsoapplicable to the cases in FIG. 11A and FIG. 11B in which the scanningpositions become dense or sparse, and the cases of combinations of FIG.9A, FIG. 9B, FIG. 11A, and FIG. 11B in which a shift and a dense orsparse state occur. FIG. 10A is an illustration of a relationshipbetween the pixel number and the scanning position, and a horizontalaxis represents a pixel number “n”, and a vertical axis “y” represents ascanning position in the sub-scanning direction, square dots beingplotted as the scanning positions on the photosensitive drum 102. InFIG. 10A, the case is described in which the scanning lines are dense onthe photosensitive drum 102 within a range of the pixel number of n≤2,and the scanning lines are sparse on the photosensitive drum 102 withina range of the pixel number of n≥2.

As illustrated in FIG. 10A, when the scanning lines are dense within therange of the pixel number of n≤2, and are sparse within the range of thepixel number of n≥2, the gradient of a straight line within the range ofthe pixel number of n≤2 is different from that of a straight line withinthe range of the pixel number of n≥2, and the straight line has a curvedshape at the pixel number of n=2. In FIG. 10A, a function indicating achange in scanning positions passing through the square dots is definedas ft(n) and is represented by the solid line. The function ft(n)representing the scanning positions is represented by Expression (14).y=ft(n)  Expression (14)

Next, when a function after the coordinate transformation of the y-axisthat represents the scanning positions in the sub-scanning direction isdefined as ft′(n), the function ft′(n) representing the scanningpositions after the coordinate transformation is represented byExpression (15).y′=ft′(n)  Expression (15)

In the embodiment, the coordinate transformation is performed byexpanding or contracting the y-axis or shifting the y-axis so that thescanning positions after the coordinate transformation become uniform.Therefore, the function ft′(n) representing the scanning positions afterthe coordinate transformation satisfies the condition represented byExpression (16).ft′(n)=n  Expression (16)

Expression (16) means that, for example, a pixel position y′ (=ft′(2))in the sub-scanning direction after the coordinate transformationbecomes 2 with respect to the pixel number 2.

The broken lines connecting FIG. 10A and FIG. 10B to each otherrepresent the correspondence from an original coordinate position of they-axis to a coordinate position of the y′-axis after the coordinatetransformation from the left to the right, and indicate a state in whicha lower half (corresponding to n≤2) of the y-axis expands, and an upperhalf (corresponding to n≥2) contracts before and after the coordinatetransformation. A procedure for determining a coordinate after thecoordinate transformation of each pixel of input image data through thecoordinate transformation of FIG. 10A and FIG. 10B will be describedwith reference to FIG. 10C and FIG. 10D. In the same manner as in FIG.10A and FIG. 10B, a horizontal axis in FIG. 10C and FIG. 10D representsa pixel number n, and a vertical axis “y” (or y′) represents scanningpositions in the sub-scanning direction. FIG. 10C is an illustrationbefore the coordinate transformation, and FIG. 10D is an illustrationafter the coordinate transformation. A relationship between the pixelnumber n and the coordinate position “y” of the input image data will bedescribed below. First, the broken line of FIG. 10C represents afunction fs(n) representing ideal scanning positions before thecoordinate transformation and is represented by Expression (17).y=fs(n)  Expression (17)

Further, in the embodiment, the interval between the pixels in thesub-scanning direction of the input image data is uniform, and hence thefunction fs(n) is represented by Expression (18).fs(n)=n  Expression (18)

A scanning position of the y′-coordinate after the coordinatetransformation of a pixel number of interest ns of the input image datais determined through three steps described below. In the first step,when the y-coordinate of an ideal scanning position corresponding to thepixel number ns of the input image data is defined as ys, ys can bedetermined by Expression (19).ys=fs(ns)  Expression (19)

A pixel number “nt” in which the scanning position before the coordinatetransformation is the same on the photosensitive drum 102 (solid line)is determined ((1) of FIG. 10C). The scanning position on thephotosensitive drum 102 is represented by the function y=ft(n), and arelationship of ys=ft(nt) holds. When an inverse function of thefunction ft(n) is defined as ft⁻¹(y), the pixel number “nt” isrepresented by Expression (20).nt=ft ⁻¹(ys)  Expression (20)

In the second step, the y′-coordinate after the coordinatetransformation (defined as “yt”) corresponding to the pixel number “nt”of the scanning position on the photosensitive drum 102 is determined byExpression (21) with use of the function ft′(n) after the coordinatetransformation ((2) of FIG. 10D).yt=ft′(nt)  Expression (21)The pixel number ns holds even when any number is selected, and hence anexpression for determining the position “yt” of the y′-coordinate afterthe coordinate transformation based on the pixel number ns correspondsto the function fs′(n) for determining the y′-coordinate in calculationbased on the pixel number n of the input image data. Thus, a generalexpression represented by Expression (22) is derived from Expressions(19) to (21). A function indicating the ideal scanning positionrepresented by the broken line after the coordinate transformation isrepresented by y′=fs′(n) ((3) of FIG. 10D).yt=fs′(ns)=ft′(nt)=ft′(ft ⁻¹(ys))=ft′(ft ⁻¹(fs(ns)))“ns” is generalized into “n” to obtain Expression (22).fs′(n)=ft′(ft ⁻¹(fs(n)))  Expression (22)

Further, Expression (18) and Expression (16) in which the pixel intervalof the input image data and the interval of the scanning positions afterthe coordinate transformation are set to be uniform, with the distanceof 1, are substituted into Expression (22). Then, Expression (22) isrepresented by Expression (23) with use of the inverse function ft⁻¹(n)of the function ft(n) for deriving the scanning position from the pixelnumber “n”.fs′(n)=ft ⁻¹(n)  Expression (23)

Expression (9) in which the scanning positions are shifted uniformly inthe advance direction and the return direction as illustrated in FIG. 9Aand FIG. 9B, and Expression (12) for determining a position after thecoordinate transformation of the input image data also have an inversefunction relationship, and it can be confirmed that Expression (23)holds. Further, when applied to the case in which the dense or sparsestate occurs in scanning positions as illustrated in FIG. 11A and FIG.11B, the function “y” representing scanning positions before thecoordinate transformation is represented by Expression (24) when thefunction “y” is a straight line with a gradient “k”, passing through(n0, y0).fs(n)=y=k×(n−n0)+y0  Expression (24)In order to determine a pixel position after the coordinatetransformation of the y-axis of the input image data, it is onlynecessary that an inverse function ((1/k)×(y−y0)+n0) be determined byExpressions (22) and (23), and the pixel number “n” be substituted intothe inverse function, and hence Expression (25) is derived.y′=(1/k)×(n−y0)+n0  Expression (25)When the scanning lines illustrated in FIG. 11A are dense, and thescanning lines illustrated in FIG. 11B are sparse, the positions of thescanning lines on the photosensitive drum 102 after the coordinatetransformation can be represented by Expression (25) in both the cases.Further, a correction value Cn of the pixel number n is determined byCn=fs′(n)−fs(n).

Specifically in FIG. 11A, n0=y0=3 and k=0.8 are satisfied, andExpression (26) is obtained.fs′(n)=(1/0.8)×(n−3)+3  Expression (26)For example, in the pixel number 3, fs′(3)=3.00 is satisfied, and thecorrection value C3 is 0.00 (=3.00−3.00). Further, in the pixel number5, fs′(5)=5.50 is satisfied, and the correction value C5 is +0.50(=+5.50−5.00). The correction values C1 to C5 when the scanningpositions are dense are illustrated in FIG. 13C.

Further, in FIG. 11B, n0=y0=3, and k=1.2 are satisfied, and Expression(27) is obtained.fs′(n)=(1/1.2)×(n−3)+3  Expression (27)For example, in the pixel number 3, fs′(3)=3.000 is satisfied, and thecorrection value C3 is 0.000 (=3.000−3.000). Further, in the pixelnumber 5, fs′(5)=4.667 is satisfied, and the correction value C5 is−0.333 (=4.667−5.000). The correction values C1 to C5 when the scanningpositions are sparse are illustrated in FIG. 13D.

Further, even when a dense or sparse state and a shift are mixed in thescanning lines, an ideal scanning position after the coordinatetransformation can be determined with use of Expression (22) or (23).The correction value setting portion 506 is configured to subject anideal scanning position to the coordinate transformation based on apositional deviation amount to determine the correction value Cn, andoutput information on the correction value Cn to the filter coefficientsetting portion 504.

(Filtering)

In the embodiment, the filtering is performed in order to generatecorrection data. In the embodiment, the filtering portion 501 isconfigured to perform the filtering through a convolution operationbased on the following filter function. That is, the filtering portion501 performs the filtering based on a positional relationship betweenthe pixel positions in the sub-scanning direction of pixels obtained bycorrecting scanning positions in the sub-scanning direction of pixels ofthe input image data, and the sub-scanning positions of pixels having aninterval between scanning lines transformed uniformly by the coordinatetransformation. A pixel before the filtering is also referred to as aninput pixel, and a pixel after the filtering is also referred to as anoutput pixel. Further, a pixel before the filtering is a pixel subjectedto the above-mentioned coordinate transformation.

The convolution function according to the embodiment can be selectedfrom linear interpolation illustrated in FIG. 12A, and bicubicinterpolation illustrated in FIG. 12B and FIG. 12C. The filter functionoutput portion 505 outputs information on the convolution function usedin the filtering to the filter coefficient setting portion 504 asinformation of the table, for example. In FIG. 12A, 12B, and FIG. 12C, avertical axis “y” represents a position in the sub-scanning direction,with a unit being a pixel, and a horizontal axis represents a magnitudeof a coefficient. Although the unit of the vertical axis “y” is set to apixel, a line may be used as a unit because the sub-scanning directionis illustrated.

An expression of FIG. 12A is represented by Expression (28).k=y+1 (−1≤y≤0)k=−y+1 (0<y≤1)0 (y<−1,y>1)  Expression (28)

Expressions of FIG. 12B and FIG. 12C are represented by the followingtwo expressions.

$\begin{matrix}{{{bicubic}(t)} = \left\{ \begin{matrix}{{\left( {a + 2} \right){t}^{3}} - {\left( {a + 3} \right){t}^{2}} + 1} & \left( {{t} \leq 1} \right) \\{{a{t}^{3}} - {5a{t}^{2}} - {8a{t}} - {4a}} & \left( {1 < {t} \leq 2} \right) \\0 & \left( {2 < {t}} \right)\end{matrix} \right.} & {{Expression}\mspace{14mu}(29)} \\{\mspace{79mu}{k = {{{bicubic}\left( \frac{y}{w} \right)}/w}}} & {{Expression}\mspace{14mu}(30)}\end{matrix}$

In the embodiment, “a” is set to −1, and “w” is set to 1 in FIG. 12B andset to 1.5 in FIG. 12C, but “a” and “w” may be adjusted in accordancewith the electrophotographic characteristics of each image formingapparatus. The filter coefficient setting portion 504 is configured tooutput a coefficient (“k” described later) to be used in the filteringto the filtering portion 501 based on the information on the filterfunction obtained from the filter function output portion 505 and theinformation on the correction value C output from the correction valuesetting portion 506. In the embodiment, the correction value C iscorrected in accordance with a developing voltage value as describedlater.

Now, the filtering will be described with reference to FIG. 12D. In FIG.12D, a horizontal axis represents a coefficient “k” to be used in thefiltering, and a vertical axis represents a position “y” in thesub-scanning direction. When the filter coefficient setting portion 504receives the correction value Cn from the correction value settingportion 506, the filter coefficient setting portion 504 determines acoefficient “kn” corresponding to the correction value Cn with use ofthe filter function input from the filter function output portion 505.White circles of FIG. 12D represent coefficients before the coordinatetransformation. Further, in FIG. 12D, it is illustrated thatcoefficients k1 and k2 were set with respect to a correction value C1and a correction value C2, respectively, as coefficients “kn” to be usedin the filtering (black circles). In the embodiment, the sameconvolution function is applied irrespective of whether the input imagedata is dense or sparse, and sampling is performed at an ideal scanningposition, to thereby store density per predetermined area of the inputimage data.

(Specific Example of Filtering)

A specific example of performing the filtering with use of theconvolution operation with a filter function by linear interpolation ofExpression (28) based on a coordinate position after the coordinatetransformation of the embodiment will be described with reference toFIG. 13A, FIG. 13B, FIG. 13C, and FIG. 13D. The filtering using theconvolution operation is performed by the filtering portion 501. FIG.13A to FIG. 13D correspond to FIG. 8A to FIG. 8D. Each column on theleft side of FIG. 13A to FIG. 13D represents input pixels after theabove-mentioned coordinate transformation. Further, each column on theright side of FIG. 13A to FIG. 13D represents scanning positions on thephotosensitive drum 102 after the above-mentioned coordinatetransformation. That is, the scanning positions in each column on theright side of FIG. 13A and FIG. 13D have been subjected to thecoordinate transformation so as to have a uniform interval and adistance of 1.

More specifically, the scanning positions in the sub-scanning directionof input pixels after the coordinate transformation are represented by astraight line (y′=fs′(n)) indicated by the alternate long and short dashline of the graph after the coordinate transformation illustrated on theright side of FIG. 9A, FIG. 9B, FIG. 11A, and FIG. 11B. The scanningpositions on the photosensitive drum 102 after the coordinatetransformation are represented by a straight line (y′=fs′(n)) indicatedby the solid line of the graph after the coordinate transformationillustrated on the right side of FIG. 9A, FIG. 9B, FIG. 11A, and FIG.11B. For example, in FIG. 9A, the shift amount is +0.2 (=S), and hencefs′(n)=y−0.2=n−0.2 is satisfied after the coordinate transformation.

Further, in FIG. 13A, FIG. 13B, FIG. 13C, and FIG. 13D, the magnitude ofa pixel value, that is, a density value is represented by shading ofcircles. Further, numbers in parentheses indicate numbers of scanninglines, and are the same as the pixel numbers illustrated in FIG. 8A toFIG. 8D. In each graph at the center of FIG. 13A, FIG. 13B, FIG. 13C,and FIG. 13D, a horizontal axis represents density, and a vertical axisrepresents a position in the sub-scanning direction. The convolutionoperation involves developing waveforms W (W1 to W5 with respect to thepixels (1) to (5)) obtained by multiplying the filter function based oneach coordinate position of an input image (FIG. 12A) by a pixel value,and adding the waveforms W by superimposing.

FIG. 13A will be described first. The pixels (1) and (5) represented bywhite circles have a density of 0, that is, a pixel value of 0.Therefore, W1 and W5 obtained by multiplying a filter function by apixel value are both 0. The pixels (2), (3), and (4) represented byblack circles have the same density, and the maximum values of thewaveforms W2, W3, and W4 are the same. Thus, the pixels (2), (3), and(4) each result in a waveform obtained by developing the filter functionbased on the pixel position of the input pixel. The result of theconvolution operation is a sum (ΣWn, n=1 to 5) of all the waveforms.

A pixel value of an output pixel is sampled at the scanning position onthe photosensitive drum 102 after the scanning position is subjected tothe coordinate transformation. Therefore, for example, the pixel value(1) corresponding to the scanning position on the photosensitive drum102 intersects with the waveform W2 at a point P0, and hence iscalculated to be density D1. Further, the pixel value (2) intersectswith the waveform W2 at a point P2 and the waveform W3 at a point P1,respectively, and hence is calculated to be density D1+D2. The pixelvalues (3) to (5) are subsequently determined in a similar manner. Thepixel value (5) does not intersect with any waveform, and hence thepixel value thereof is set to 0. Further, the result obtained bycalculating the pixel values (1) to (5) of FIG. 13B to FIG. 13D arerepresented by shading of pixels in each column on the right side.

The positional deviation of the input pixels is illustrated so as tocorrespond to each pixel in the vertical axis of FIG. 13A to FIG. 13D.The positional deviation amount represented by the vertical axis of FIG.13A to FIG. 13D is information on the positional deviation amountdetermined by an inverse function in accordance with the coordinatetransformation of the scanning positions in the sub-scanning directionof the pixels of the input image. For example, in the case of FIG. 13A,as described with reference to FIG. 9A, the correction amount C of thepositional deviation amount S of the scanning lines is −0.2. Further,for example, in the cases of FIG. 13C and FIG. 13D, the correctionamounts C are calculated with use of Expressions (26) and (27),respectively.

FIG. 13A is an illustration of a state in which the scanning positionsof the scanning lines are shifted in the advance direction in thesub-scanning direction, but the gravity centers of the pixel values areshifted in the return direction, and hence the positions of the gravitycenters of the pixel values are corrected. FIG. 13B is an illustrationof a state in which the scanning positions of the scanning lines areshifted in the return direction in the sub-scanning direction, but thegravity centers of the pixel values are shifted in the advancedirection, and hence the positions of the gravity centers of the pixelvalues are corrected. FIG. 13C is the case in which the scanningpositions are dense, and is an illustration of a state in which thedistribution of density is widened due to the convolution operationafter the coordinate transformation to cancel the local concentration ofdensity, to thereby correct a local change in density. Further, FIG. 13Dis the case in which the scanning positions are sparse, and is anillustration of a state in which the distribution of density is narroweddue to the convolution operation after the coordinate transformation tocancel the dispersion of density, to thereby correct a local change indensity. In particular, the pixel value (3) of FIG. 13D is a density of(100+α) % that is higher than 100%.

(Filtering)

Referring back to FIG. 7, in Step S3605, the CPU 303 selects and reads,from a correction table shown in Table 2, a position correctioncoefficient h1 and a light intensity correction coefficient h2corresponding to the setting value of the developing voltage read inStep S3603 described above. The CPU 303 is configured to store thecorrection table shown in Table 2 in an internal storage portion (notshown) of the CPU 303.

TABLE 2 Position Light Intensity Developing Correction CorrectionVoltage Coefficient h1 Coefficient h2 −500 V 0.9 0.9 −450 V 1 1 −400 V1.1 1.1 −350 V 1.2 1.2

Table 2 is an example of a correction table regarding the setting valueof the developing voltage. In Table 2, the left column represents thedeveloping voltage value of a developing voltage applied by thedeveloping device 105, and the center column represents the positioncorrection coefficient h1 for correcting a position correction amount(deviation amount of a scanning line) in accordance with the developingvoltage value. Further, the right column of Table 2 represents the lightintensity correction coefficient h2 for correcting image data indicatingimage density in accordance with the developing voltage value. Thedeveloping voltage value is held within a range of from −350 V to −500 Vin a unit of 50 V (volts), but the developing voltage value may be heldin a smaller developing voltage unit in Table 2. Further, in theembodiment, the above-mentioned developing threshold value Th is set toa light intensity (exposure amount) at a time when the developingvoltage is −450 V. Therefore, in Table 2, when the developing voltage is−450 V, coefficients (h1=1, h2=1), at which the position correction andthe light intensity correction are not performed, are set. Meanwhile,when the developing voltage is not −450 V, correction is made with theposition correction coefficient h1 and the light intensity correctioncoefficient h2 shown in Table 2, and the position correction amount thatis a deviation amount of a scanning line and the pixel value (pixeldata) that is a density value of a pixel are adjusted.

The CPU 303 is configured to obtain the position correction coefficienth1 and the light intensity correction coefficient h2 corresponding tothe current developing voltage value from Table 2 and corrects (adjusts)the position correction amount and the image data by Expressions (31)and (32).Position correction amount′=Position correction amount×Positioncorrection coefficient h1  Expression (31)Image data′=Image data×Light intensity correction coefficienth2  Expression (32)

The position correction amount of Expression (31) refers to theabove-mentioned correction amount C, and the image data of Expression(32) refers to the image density of a pixel.

In Step S3606, the CPU 303 performs the filtering with the filteringportion 501 based on attribute information for correction (positioncorrection amount, position correction amount′ after adjustment of imagedata, image data′) generated in Step S3605. More specifically, the CPU303 performs the above-mentioned convolution operation and re-sampling(correction of image data of an output image) for the input image. Asdescribed above, in the embodiment, the CPU 303 corrects the positioncorrection amount and the image data in accordance with the developingvoltage value.

In the embodiment, when the setting value of the developing voltage(absolute value) becomes larger (e.g., −500 V) than −450 V (voltage atwhich the developing threshold value Th is obtained), the developingthreshold value Th decreases. In contrast, when the setting value of thedeveloping voltage (absolute value) becomes smaller (e.g., −400 V, −350V) than −450 V, the developing threshold value Th increases. When thedeveloping threshold value Th decreases, development is performedthrough adhesion of a toner even when the light intensity is small, andhence the image density increases, with the result that the gravitycenter movement amount in the case of an image shift becomes larger.Therefore, as the developing voltage increases (e.g., −500 V), theposition correction coefficient h1 and the light intensity correctioncoefficient h2 are set to be smaller than 1 so that the image density isdecreased, and the gravity center movement amount in the case of animage shift becomes smaller.

Meanwhile, when the developing threshold value Th increases, a tonerdoes not adhere unless the light intensity is increased, and hence theimage density decreases, with the result that the gravity centermovement amount in the case of an image shift becomes smaller.Therefore, as the developing voltage decreases (e.g., −350 V, −400 V),the position correction coefficient h1 and the light intensitycorrection coefficient h2 are set to be larger than 1 so that the imagedensity is increased, and the gravity center movement amount in the caseof an image shift becomes larger.

The position correction coefficient h1 and the light intensitycorrection coefficient h2 shown in Table 2 represent examples of valuesset based on the characteristics obtained through an experiment. Forexample, when the sensitivity characteristics are varied depending onthe difference in developing method and material for the photosensitivedrum, the values and magnitude relationship of the respective correctioncoefficients shown in Table 2 are also varied. Therefore, when thedeveloping method and the material for the photosensitive drum aredifferent, it is only necessary that a relationship of the image densityand the gravity center movement amount be determined in advance for eachimage forming condition (e.g., developing voltage, charging voltage, andexposure light intensity), to thereby determine a correctioncoefficient.

As described above, when a position correction amount and image densityfor correcting banding are corrected based on the setting value of adeveloping voltage, banding can be corrected without causing unevenimage density and the like even when a developing threshold valuechanges. In the above-mentioned embodiment, an example in whichcorrection is made with use of a developing voltage value as the imageforming condition will be described. For example, in an image formingapparatus in which a charging voltage and an exposure amount areadjusted so as to adjust image density, in the same way as in Table 2, acorrection table corresponding to the charging voltage and the exposureamount may be provided so as to correct a position correction amount andimage density in accordance with the charging voltage and the exposureamount. Thus, by switching a correction coefficient of bandingcorrection in accordance with the image forming conditions, an imagedefect, e.g., an error of the gravity center movement amount of an imageor a density change, which occurs due to a change in image formingcondition, can be prevented.

Further, there is an image forming apparatus having a configuration inwhich the thermistor 401 is arranged in a main body, and the imageforming conditions (developing voltage, charging voltage, and exposureamount) are controlled in accordance with the temperature detectionresults obtained by the thermistor 401. In the image forming apparatushaving such configuration, the temperature detection informationobtained by the thermistor 401 may be associated with the positioncorrection coefficient information and the light intensity correctioncoefficient information and stored, and a position correction amount andimage density may be corrected in accordance with the temperaturedetection results obtained by the thermistor 401.

Further, besides the linear interpolation and bicubic interpolation usedas interpolation method of the embodiment, interpolation in which awindow function of a desired size is applied to a Sinc function orinterpolation involving determining a convolution function in accordancewith intended filter characteristics may be performed. Further, thepresent invention can be applied to an image output method or an imageoutput device in which an interval between output pixels or lines isdistorted, irrespective of whether the method is an LED exposure methodor an electrophotographic method. Further, in the embodiment,interpolation is performed by correcting a position of a pixel of aninput image in accordance with Expressions (22) and (23), but functionsapproximate to Expressions (22) and (23) may be selected to be used forcorrection depending on the intended correction accuracy. Further, theconfiguration using the CPU 303 as the controller is described, but anapplication specific integrated circuit (ASIC), for example, may beused.

As described above, according to the embodiment, satisfactory imagequality can be obtained by correcting distortion and uneven imagedensity of an image in accordance with the image forming conditions.

Second Embodiment

In the first embodiment, a method involving correcting a gravity centermovement amount in the case of an image shift and image density inaccordance with a developing voltage will be described. In the secondembodiment, a method involving detecting a change in developingthreshold value with the density sensor 602 arranged in the imageforming apparatus 100 and correcting a gravity center movement amount inthe case of an image shift and image density in accordance with thedeveloping threshold value will be described. The configurations of theimage forming apparatus 100 and the light scanning device 104 are thesame as those of the first embodiment. Therefore, those configurationsare denoted by the same reference symbols, and the description thereofis omitted.

<Density Sensor>

FIG. 14A is a schematic view for illustrating a positional relationshipof the density sensor 602. The density sensor 602 is installed in anupper portion at a position opposed to a center portion of theintermediate transfer belt 107 in a direction orthogonal to therotational direction. The density sensor 602 is configured to detectdensity of a density detection patch 603 formed in the center portion ofthe intermediate transfer belt 107 and output the detected density valueof the density detection patch 603 to the CPU 303.

<Relationship Between Exposure Light Intensity and Image Density>

In the embodiment, the CPU 303 is configured to form a plurality ofpatch images on the intermediate transfer belt 107 with the lightscanning device 104 with a change in exposure amount of the lightscanning device 104 and detect density values of the patch images withthe density sensor 602. FIG. 14B is a graph for showing a characteristiccurve representing the relationship between the exposure amount in whichthe light scanning device 104 exposes the photosensitive drum 102 withlight and the image density of the patch images (patches 1 to 5) formedon the intermediate transfer belt 107. The vertical axis of FIG. 14Brepresents image density, and the horizontal axis represents lightintensity (exposure amount). FIG. 14B is a graph for showing detectionresults obtained by forming patch images (patches 1 to 5) with the lightscanning device 104 with a change in exposure amount of the lightscanning device 104 in five stages and detecting image density of eachpatch image with the density sensor 602. The CPU 303 is configured tointerpolate the relationship between the density value of each patch andthe exposure amount and determine an exposure amount Phalf in which theimage density of a patch to be formed becomes 50% with respect to thepatch 1 having an image density of 100% (largest). In this case, theexposure amount Phalf in which the image density becomes 50% refers toan exposure amount at a time of forming an image having intermediatedensity between solid black (patch 1 of FIG. 14B) in which a toner is inthe thickest state and solid white in which a toner is not present(toner non-adhesion state). In the embodiment, in the exposure amountPhalf in which the intermediate density is obtained, an exposure amountPhalf corresponding to 50% of the exposure amount at a time of formingthe patch 1 (solid black patch) having an image density of 100% isdefined as the developing threshold value Th. A correction tablecontaining information, in which the position correction coefficient h1and the light intensity correction coefficient h2 are associated witheach exposure amount Phalf, is stored in the internal storage portion(not shown) of the CPU 303. Table 3 is an example of such correctiontable.

TABLE 3 Position Light Intensity Correction Correction Phalf Coefficienth1 Coefficient h2 30% 1.2 1.2 40% 1.1 1.1 50% 1 1 60% 0.9 0.9 70% 0.80.8

In Table 3, the left column represents a numerical value indicating, interms of percent, the exposure amount Phalf corresponding to 50% of theimage density when the exposure amount at a time of forming the patch 1(solid black patch) is defined as 100%. Further, the center column ofTable 3 represents the position correction coefficient h1 correspondingto each exposure amount, and the right column of Table 3 represents thelight intensity correction coefficient h2 corresponding to each exposureamount. The exposure amount is held within a range of from 30% to 70% inincrements of tens percent (10%), but the exposure amount may be held ina smaller unit (e.g., 5%) in Table 3. Further, in Table 3, the lightintensity at a time when the exposure amount Phalf is 50% is defined asthe developing threshold value Th, and hence coefficients (h1=1, h2=1),at which the position correction and the light intensity correction arenot performed, are set. Meanwhile, when the exposure amount Phalf is not50%, the position correction coefficient h1 and the light intensitycorrection coefficient h2 for performing the position correction and thedensity correction in accordance with an exposure amount are set.

In the embodiment, the exposure amount which is 50% of the exposureamount at a time of forming a solid black patch is defined as thedeveloping threshold value Th. Therefore, when the exposure amount Phalfbecomes smaller (e.g., 30%, 40%) than the developing threshold value Th,the developing threshold value Th increases. Therefore, the adhesion ofa toner does not occur easily, and image density decreases. In view ofthe foregoing, the position correction coefficient h1 and the lightintensity correction coefficient h2 are set to be larger than 1 so thatthe image density is increased, and the gravity center movement amountin the case of an image shift becomes larger. Meanwhile, when theexposure amount Phalf becomes larger (e.g., 60%, 70%) than thedeveloping threshold value Th, the developing threshold value Thdecreases, and hence a larger amount of toner can be adhered easily, andthe image density is increased. Therefore, the position correctioncoefficient h1 and the light intensity correction coefficient h2 are setto be smaller than 1 so that the image density is decreased, and thegravity center movement amount in the case of an image shift becomessmaller.

Also in the embodiment, the CPU 303 is configured to correct an imageposition and image data by reading the processing of the flowchart ofFIG. 7 described in the first embodiment as described below. That is, inthe embodiment, in Step S3603, the CPU 303 reads the exposure amountPhalf in which the image density becomes 50%, which is determined fromthe density value of a patch image detected by the density sensor 602,instead of reading the developing voltage setting value. Further, inStep S3605, the CPU 303 selects and obtains the position correctioncoefficient h1 and the light intensity correction coefficient h2corresponding to the exposure amount Phalf from Table 3 and calculates aposition correction amount′ and image data′ by Expressions (31) and(32). A series of operations of forming patches and detecting thedensity of the formed patches is controlled for execution timing by theCPU 303 and are executed, for example, at timing before image formation,such as timing immediately after the image forming apparatus 100 isturned on. Then, the exposure amount Phalf determined at this time, inwhich the image density becomes 50%, is stored in the internal storageportion (not shown) of the CPU 303.

In the embodiment, there is described a method involving detecting theexposure amount Phalf in which the image density becomes 50%, to therebypredict a difference in exposure amount from the developing thresholdvalue Th, and correcting the position correction amount and the imagedata. Detection of the image density of a plurality of patch imagesobtained with a change in exposure amount enables prediction of adifference in exposure amount from the developing threshold value Thwith higher accuracy. As a result, the image position and the imagedensity can be corrected with high accuracy. In the embodiment, theexposure amount Phalf that is 50% of the exposure amount at a time offorming a solid black patch is closest to the developing threshold valueTh, and hence the position correction coefficient h1 and the lightintensity correction coefficient h2 are determined in accordance withthe exposure amount Phalf. For example, a level different from thedensity of 50% may be set to be the developing threshold value Thdepending on the developing characteristics of the image formingapparatus.

As described above, according to the embodiment, satisfactory imagequality can be obtained by correcting uneven image density of an imagecaused in a direction corresponding to the rotational direction of thephotosensitive member in accordance with the image forming conditions.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2015-141774, filed Jul. 16, 2015, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. A correction method for an image formingapparatus, the image forming apparatus comprising: a light sourcecomprising a plurality of light emitting points; a photosensitive memberconfigured to rotate in a first direction so that a latent image isformed on the photosensitive member with a light beam emitted from thelight source; and a deflecting unit configured to deflect the light beamemitted from the light source to move light spots of the light beamradiated to the photosensitive member in a second direction orthogonalto the first direction to form scanning lines, the correction methodcomprising a correction step of correcting sparseness and denseness ofdensity in the first direction, the sparseness and denseness of densityin the first direction having been caused by deviation of the scanninglines in the first direction, by moving a pixel of interest in the firstdirection in accordance with the deviation of the scanning lines, and anoutput step of causing a pixel value of the pixel of interest to beoutput in accordance with a movement of the pixel of interest, wherein acorrection amount of the pixel value of the pixel of interest differs inaccordance with an image forming condition.
 2. A correction methodaccording to claim 1, wherein the image forming apparatus furthercomprises a developing device configured to develop the latent image onthe photosensitive member to form a toner image, wherein the imageforming condition comprises a developing voltage applied to thephotosensitive member by the developing device, and wherein thecorrection amount of the pixel value of the pixel of interest when thedeveloping voltage is higher than a predetermined voltage is adjusted soas to be smaller than the correction amount of the pixel value of thepixel of interest when the developing voltage is the predeterminedvoltage.
 3. A correction method according to claim 1, wherein the imageforming apparatus further comprises a charging device configured tocharge the photosensitive member with a uniform voltage, wherein theimage forming condition comprises a charging voltage with which thecharging device charges the photosensitive member, and wherein thedeviation of the scanning lines and the correction amount of the pixelvalue of the pixel of interest are adjusted in accordance with thecharging voltage.
 4. A correction method according to claim 1, whereinthe image forming condition comprises a light intensity of the lightbeam emitted from the light source to the photosensitive member, andwherein the deviation of the scanning lines and the correction amount ofthe pixel value of the pixel of interest are adjusted in accordance withthe light intensity.
 5. A correction method according to claim 1,wherein the image forming apparatus further comprises a temperaturedetection unit configured to detect temperature of the image formingapparatus, wherein the image forming condition comprises the temperatureof the image forming apparatus, and wherein the deviation of thescanning lines and the correction amount of the pixel value of the pixelof interest are adjusted in accordance with the temperature detected bythe temperature detection unit.
 6. A correction method according toclaim 1, wherein the image forming condition comprises a light intensityof the light beam emitted from the light source to the photosensitivemember at a time when image density is predetermined density, andwherein when the light intensity is larger than a predetermined lightintensity, the deviation of the scanning lines and the correction amountof the pixel value of the pixel of interest are adjusted so as to besmaller than the deviation of the scanning lines and the correctionamount of the pixel value of the pixel of interest at a time when thelight intensity is the predetermined light intensity, and when the lightintensity is smaller than the predetermined light intensity, thedeviation of the scanning lines and the correction amount of the pixelvalue of the pixel of interest are adjusted so as to be larger than thedeviation of the scanning lines and the correction amount of the pixelvalue of the pixel of interest at the time when the light intensity isthe predetermined light intensity.
 7. A correction method according toclaim 6, wherein the image forming apparatus further comprises a densitydetection unit configured to detect density of a patch image, andwherein the light intensity of the light beam radiated to thephotosensitive member so that the image density reaches thepredetermined density is determined based on detection results ofdensities of patch images detected by the density detection unit, thepatch images being formed through exposure with a plurality of differentlight intensities of the light beam.
 8. A correction method according toclaim 7, wherein the predetermined density comprises densitycorresponding to 50% when density of a solid black patch image detectedby the density detection unit is defined to be 100%.
 9. A correctionmethod according to claim 8, wherein the predetermined light intensitycomprises a light intensity corresponding to 50% when a light intensityof the light beam emitted from the light source to the photosensitivemember in order to form the solid black patch image is defined to be100%.
 10. A correction method according to claim 1, wherein thecorrection step comprises: a storing step of storing, in a storage unit,information on positional deviation of the scanning lines in the firstdirection; a conversion step of converting positions of pixels of aninput image by performing coordinate transformation based on theinformation stored in the storage unit so that an interval between thescanning lines on the photosensitive member becomes a predeterminedinterval; an adjustment step of adjusting the positions of the pixels ofthe input image after the coordinate transformation and pixel values ofthe pixels of the input image in accordance with the image formingcondition; and a filtering step of determining pixel values of pixels ofan output image by subjecting the pixel values of the pixels of theinput image after the adjustment to a convolution operation based on thepositions of the pixels of the input image after the adjustment.
 11. Acorrection method according to claim 10, wherein the conversion stepcomprises determining the positions of the pixels of the input imageafter the coordinate transformation with use of an inverse functionft⁻¹(n) of a function ft(n) by the following expression:fs′(n)=ft′(ft ⁻¹(fs(n))) where: fs(n) represents a function indicating aposition of an n-th pixel in the first direction of the input image;ft(n) represents a function indicating a position of the n-th pixel inthe first direction of the output image; fs′(n) represents a functionindicating a position of the n-th pixel in the first direction of theinput image after the coordinate transformation; and ft′(n) represents afunction indicating a position of the n-th pixel in the first directionof the output image after the coordinate transformation.
 12. Acorrection method according to claim 11, wherein the conversion stepcomprises determining, when the function fs(n) satisfies fs(n)=n and thefunction ft′(n) satisfies ft′(n)=n, the positions of the pixels of theinput image after the coordinate transformation by the followingexpression:fs′(n)=ft ⁻¹(n).
 13. A correction method according to claim 11, whereinthe conversion step comprises interpolating, when the function fs(n)indicating the positions of the pixels of the input image or thefunction ft(n) indicating the positions of the pixels of the outputimage takes discrete values, the discrete values to obtain a continuousfunction.
 14. A correction method according to claim 10, wherein thefiltering step comprises performing the convolution operation with useof linear interpolation or bicubic interpolation.
 15. A correctionmethod according to claim 10, wherein the pixel values comprise densityvalues, and wherein the filtering step comprises storing density valuesper predetermined area before and after performing the convolutionoperation.
 16. A correction method according to claim 10, wherein theimage forming apparatus further comprises a speed detection unitconfigured to detect a rotation speed of the photosensitive member, andwherein the positional deviation in the first direction is correctedbased on the rotation speed of the photosensitive member detected by thespeed detection unit.
 17. A correction method according to claim 10,wherein the deflection unit comprises a rotary polygon mirror having apredetermined number of faces, and wherein the information to be storedin the storage unit contains information on a variation in angle foreach of the faces with respect to a rotary shaft of the rotary polygonmirror.
 18. A correction method according to claim 10, wherein thepredetermined interval is determined in accordance with a resolution ofimage formation by the image forming apparatus.
 19. A correction methodfor an image forming apparatus comprising a light source including aplurality of light emitting points, a photosensitive member configuredto rotate in a first direction so that a latent image is formed on thephotosensitive member with a light beam emitted from the light source, adeflecting unit configured to deflect the light beam emitted from thelight source to move light spots of the light beam radiated to thephotosensitive member in a second direction orthogonal to the firstdirection to form scanning lines, and a developing device configured todevelop the latent image on the photosensitive member to form a tonerimage, the correction method comprising: a correction step of correctingsparseness and denseness of density in the first direction, thesparseness and denseness of density in the first direction having beencaused by deviation of the scanning lines in the first direction, bymoving a predetermined pixel in the first direction in accordance withthe deviation of the scanning lines, and an output step of causing apixel value of the predetermined pixel to be output in accordance with amovement of the predetermined pixel, wherein the correction stepcomprises correcting, based on the deviation of the scanning lines andthe pixel value of the pixel, which are adjusted in accordance with animage forming condition, the sparseness and denseness of the density,wherein the image forming condition comprises a developing voltageapplied to the photosensitive member by the developing device, andwherein when the developing voltage is higher than a predeterminedvoltage, the deviation of the scanning lines and the pixel value of thepixel are adjusted so as to be smaller than the deviation of thescanning lines and the pixel value of the pixel at a time when thedeveloping voltage is the predetermined voltage, and when the developingvoltage is lower than the predetermined voltage, the deviation of thescanning lines and the pixel value of the pixel are adjusted so as to belarger than the deviation of the scanning lines and the pixel value ofthe pixel at the time when the developing voltage is the predeterminedvoltage.